具有两个不同标号输出类的数值系统建模
Modelling Numerical Systems with Two Distinct Labelled Output Classes
摘要：
我们提出了一种新的方法建模数值系统，有两个不同的输出解决方案类，例如临界点或分叉。高斯过程仿真是一个有用的工具，在理解这些复杂的系统，并提供估计的不确定性，但我们的目标是包括系统的两个输出解决方案之间存在不连续性。由于连续性假设，我们考虑当前的分类方法将输入空间分成两个输出区域。目前的分类和逻辑斯谛回归方法依赖于从独立的伯努利分布中提取，这忽略了邻近地区的任何已知信息。我们通过包括输入点之间的相关性来建立这一点。高斯过程仍然是一个重要的元素，但在潜在空间中使用的模型的两个区域。使用输入值和相关联的输出类标签，使用MCMC采样和唯一似然估计潜在变量。阈值（通常为零）定义了边界。我们将我们的方法应用于与哺乳动物生殖系统相关的激素所提供的一个激励性例子，其中两种解决方案与高和低的繁殖率相关。
英文摘要：
We present a new method of modelling numerical systems where there are two distinct output solution classes, for example tipping points or bifurcations. Gaussian process emulation is a useful tool in understanding these complex systems and provides estimates of uncertainty, but we aim to include systems where there are discontinuities between the two output solutions. Due to continuity assumptions, we consider current methods of classification to split our input space into two output regions. Classification and logistic regression methods currently rely on drawing from an independent Bernoulli distribution, which neglects any information known in the neighbouring area. We build on this by including correlation between our input points. Gaussian processes are still a vital element, but used in latent space to model the two regions. Using the input values and an associated output class label, the latent variable is estimated using MCMC sampling and a unique likelihood. A threshold (usually at zero) defines the boundary. We apply our method to a motivating example provided by the hormones associated with the reproductive system in mammals, where the two solutions are associated with high and low rates of reproduction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
